Consider the following mathematical model:N(O) =K0,N(O+R) =K1,where O is a rational tangle or the sum of two rational tangles,and R is a rational tangle,in addition,O and R are unknown tangles,N is the numerator construction of the tangle,and Ki (i =0,1) are the known knots or links.Give the solutions of these tangle equations that one of K0,K1is b(1,0) or b(0,1).Furthermore,one can obtain the DNA recombination model.